Collineations and Conic Sections

“The text is organised into fiffteen chapters and deals with a wealth of classical topics. … The explicit exposition of all these topics is carried out in view of their history. The reader will find detailed information about Euclid's Elements and the treatment of conic sections by Greek mathematicians such as Apollonius of Perga and Archimedes.” (Hans Havlicek, Mathematical Reviews, April, 2022)“This is a historically very well informed look at projective geometry, central collineations, and conics. The reader is exposed to both a wealth of results in projective geometry and to the motivations behind them … . The author has rendered a genuine service to the reader interested in this topic, as there is no contemporary book one could turn to both learn the basic techniques of projective geometry and to find out about its historical intricacies.” (Victor V. Pambuccian, zbMATH 1460.51001, 2021)

• Preface.- 1. Introduction.- 2. Central Collineations.- 3. The Geometry of Euclid's Elements.- 4. Conics in Greek Geometry.- 5. Conic Sections in Early Modern Europe.- 6. Conic Sections in Early Modern Europe.- 7. Central Collineations.- 8. Nineteenth Century.- 9. Foci.- 10. Steiner. 11. Desargues and Involution.- 12. Looking Ahead.- 13. Matrices and Homogeneous Coordinates.- 14. Some Applications of Conics in History.- 15. Vertical Stretch and Isaac Newton's Conics.- 16. Three Appendices.- Bibliography.